Use our free GCF of Fractions Calculator tool to compute the GCF of 87/42, 259/13, 486/567 i.e 1/14742 easily. The following is the detailed procedure to determine the greatest common factor of fractions 87/42, 259/13, 486/567.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 87/42,259/13,486/567
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 87/42,259/13,486/567, numerators are 87,259,486
Denominators are 42,13,567
The GCF of 87,259,486 is 1 .
LCM of 42,13,567 is 14742.
The greatest common factor of 87/42,259/13,486/567 = [GCF of 87,259,486]/[LCM of 42,13,567]= 1/14742
Therefore, the GCF of 87/42,259/13,486/567 is 1/14742.
To find the highest common factor of 87,259,486, we have to find the factors of both numbers and list the highest common factor.
The factors of 87 are 1, 3, 29, 87
The factors of 259 are 1, 7, 37, 259
The factors of 486 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486
The HCF of 87,259,486 is 1.
Lets's calculate GCF of 87,259,486
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 87
:1,3,29,87
Now, list down the factors of 259
:1,7,37,259
Now, list down the factors of 486
:1,2,3,6,9,18,27,54,81,162,243,486
Greatest Common Factor
We found the factors 87,259,486 . The biggest common factor number is the GCF number.
So the greatest common factor 87,259,486 is 1.
Lets's calculate LCM of 42,13,567
3 | 42, 13, 567 |
7 | 14, 13, 189 |
2, 13, 27 |
∴ So the LCM of the given numbers is 3 x 7 x 2 x 13 x 27 = 14742
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14742
Therefore, the GCF of Fractions 87/42,259/13,486/567 is 1/14742
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 42,13,567 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,13,567) = 1
common factors(in case of two or more numbers have common factors) = 21
GCF(42,13,567) x common factors =1 x 21 = 21
LCM(42,13,567) = ( 42 × 13 × 567 ) / 21
LCM(42,13,567) = 309582 / 21
LCM(42,13,567) = 14742
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 87,259,486?
The HCF of 87,259,486 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 87/42, 259/13, 486/567?
Answer: GCF of Numerators as per given numbers 87/42, 259/13, 486/567 is
GCF of Numerators i.e. for 87,259,486 is 1
LCM of denominators i.e. for 42,13,567 is 14742.
Thus, GCF of Fractions is 1/14742.Finally, GCF of Fractions for 87/42, 259/13, 486/567 is 1/14742.